What is the difference between a subdivision surface modifier and multiresolution modifier?
When using the sculpt tool, you will sometimes want to add more detail than your mesh has vertices to support.  You could add vertices by subdividing the mesh, but subdividing the mesh will increase the complexity of the model, slowing blender down, making the model larger, making the mesh less usable for certain applications (like games).

Sub surface allows you to increase the vertices as a modify, but isn't affected by sculpting.  It's purpose is to add geometry to the whole mesh and make a lower poly figure a higher quality without increasing the complexity of the mesh. You cannot move, alter or sculpt the new vertices without applying the subsurface. It wasn't designed for it.

Multi resolution modifier was added to allow you to add geometry for the purposes of adding detail to a sculpt. Vertices in a multi res modifier are affected by a sculpt even when not applied.  This allows you to sculpt with more verts than the base mesh has.  This is useful because you sculpt at a higher resolution, bake out the sculpt as a map, and apply it to the mesh as a normal map, without increasing the actual number of vertices the mesh has.

So, if you're not sculpting, sub surface and multi resolution are logically equivalent, and the preference is for sub surface (less data in memory, easier interface).  If you are sculpting, and want to keep the mesh low poly, but need more detail in the sculpt, use multi resolution and then bake out the normal map (which can then be applied to the surface of the object as a texture in the cycles node editor).